Answer
Fill in the blank
First :- $x+2$
Second :- $x+8-6\sqrt{x-1}$.
Work Step by Step
The given equation is
$\Rightarrow \sqrt{x+2}=3-\sqrt{x-1}$
Square the left hand side.
$=(\sqrt{x+2})^2$
Eliminate the radical.
$=x+2$
Square the right hand side.
$=(3-\sqrt{x-1})^2$
Use the formula $(A-B)^2=A^2-2AB+B^2$.
We have $A=3$ and $B=\sqrt{x-1}$
$=(3)^2-2(3)(\sqrt{x-1})+(\sqrt{x-1})^2$
Use product rule.
$=9-6\sqrt{x-1}+x-1$
Simplify.
$=x+8-6\sqrt{x-1}$.
